Improved Accurate Extrinsic Calibration Algorithm of Camera and Two-dimensional Laser Scanner

Transcription

1 JOURNAL OF MULTIMEDIA, VOL. 8, NO. 6, DECEMBER Improved Aurate Extrns Calbraton Algorthm of Camera and Two-dmensonal Laser Sanner Janle Kong, Le Yan*, Jnhao Lu, Qngqng Huang, and Xaokang Dng College of Tehnology, Beng Forestry Unversty, Beng, Chna Emal: *Correspondng Author Abstrat In the objet detetng system omposed of a amera and a two-dmensonal laser sanner (DLS), the extrns albraton s an essental step to operate properly. However, the edge ponts of objet annot be deteted aurately by DLS due to angular resoluton lmt, whh aused loss of auray of the extrns albraton between amera and DLS. In ths paper a new algorthm s proposed to solve ths problem. Frstly, the least-squares method was appled to lnearly ft laser data loated on the sannng plane of the three-dmensonal retangular albraton objet. Seondly, half of the value of angular resoluton was used as the angular nremental omponent of the laser edge ponts of objet to mprove the auray of laser data aptured by DLS. Fnally a general optmzaton was proposed to refne the extrns albraton parameters of amera-dls by mnmzng the re-projeton error between those adjusted laser ponts and ther orrespondng projetons under the mage oordnate of the amera. Compared wth related methods, expermental results showed that the auray of extrns albraton between amera and DLS was sgnfantly mproved. Index Terms Two-dmensonal Laser Sanner; Auray of Extrns Calbraton; Rangng Error; Step-angular Error; Camera I. INTRODUCTION In the reent studes, ombnaton of a amera and a two-dmensonal laser sanner (DLS) has been wdely used to provde applatons n deteton [1], autonomous vehle navgaton [], robot moton and ontrol [3] and 3D vsualzaton measurement [4]. In the amera-dls objet detetng system, DLS provdes real tme rangng measurements n a wde angular feld whle a amera provdes rh vsual nformaton. In order to effetvely fuson the data from the amera and DLS, t s mportant to know ther relatve poston and orentaton from eah other, whh affets the geometr nterpretaton of ther measurements. The albraton between amera and DLS an be deomposed nto ntrns albraton parameters and extrns albraton parameters. The extrns albraton parameters are the rotaton and translaton of some fdual oordnate systems relatve to the sensors. And the ntrns albraton parameters, suh as the albraton matrx of a amera, affet how the sensor samples the sene. Ths work assumes the ntrns albraton s known as the perspetve pnhole model, and fouses on the auray mprovement of the extrns albraton, whh s rtal to be solved. u p(u,v) v Image n CCD Camera Y l Pl(x l,y l) a 1 a X l Laser Data n DLS K Y CCD Camera (Φ,Δ ) Zl P Pl a (R,T) X Z Y l X l D Laser Sanner(DLS ) Fgure 1. Shemat of the extrns albraton problem of amera-dls. The three-dmensonal retangular albraton objet was posed n the both vews of the amera and DLS. Ths paper redues the rangng error and the step-angular error to mprove the laser data used for extrns albraton. The goal of ths paper s to study a new algorthm to mprove the auray of extrns albraton by refnng the rotaton matrx and the transformed vetor wth those modfed laser data. A large number of researhers have ontrbuted many works on detetng some spef ponts or strpes to solve the amera-dls extrns albraton. Those feature ponts or shapes were obtaned to establsh a homogeneous transformaton between the DLS oordnate and the amera oordnate [5-7]. However, the extraton proess of orrespondng data pars was umbersome and tme-onsumng, and the proedure of extrns albraton was naurate. To smplfy the albraton proess, the most wdely used method was proposed by Zhang and Pless n [8], and desrbed a amera-dls extrns albraton proedure where a hekerboard pattern was freely plaed n same vews smultaneously of the two sensors. For eah varous postons of the planar pattern, the method onstraned the extrns parameters by regsterng the laser sanlne on the planar pattern wth the estmated pattern plane from the amera mage. The soluton of equatons provded an Pw Zw Xw Yw do: /jmm

2 778 JOURNAL OF MULTIMEDIA, VOL. 8, NO. 6, DECEMBER 013 ntal estmate for the relatve rotaton and translaton, whh was subsequently refned by teratve mnmzaton of the re-projeton error. However, ths algorthm exsted for a problem that t needed a spef orentaton of albraton plate to obtan the optmal results, whh was dffult to be establshed. Sne the method was based on lnear equatons whh dd not dretly enfore the rotaton and translaton matrx. It often leaded to poor ntalzaton of the data pars orrespondng to the DLS data and the mages vewed by the amera, and the estmaton errors of the data pars would affet the albraton auray also. An algorthm for extrns albraton has been proposed to establsh a oordnate transform relatonshps by usng straght lne features by L n [9]. The method desgned a rght-angled trangular hekerboard to employ the nvsble nterseton ponts of the sle plane obtaned by DLS wth the edges of the hekerboard to set up the onstrants equatons. The extrns parameters are then albrated by mnmzng the algebra errors between the measured ntersetons ponts and ther orrespondng projetons on the mage plane of the amera. However, the hekerboard used n ths method was unsutable for ntrns albraton, whh was also not onvenent n extrns albraton. Another method proposed by F. Vasonelos n [10] ft lnes to the laser depth readngs and arred the Euldean regstraton of 3 planes wth 3 o-planar lnes n an optmal and losed-form manner. It s proved for the frst tme that the algnment of 3 plane-lne orrespondenes had at most 8 solutons, whh determned the rotaton and translaton by solvng a standard p3p problem. u O1 v O(u0,v 0) p(u,v) Y X f O Y X Optal Axs Z Pw(Xw,Yw,Zw) Fgure. Geometry of perspetve projeton n amera model. In mahne vson system, the transformaton of objets from the world oordnates to the pxel oordnates nvolves four referene oordnate systems: pxel oordnate system, mage oordnate system, amera oordnate system, and world oordnate system [13]. Ths work solves ntrns albraton parameters wth Matlab. However, the naurate measurement of DLS aused loss of auray of the extrns albraton between the amera and DLS severely. When a sngle laser pulse of DLS was sent out and refleted by an objet surfae wthn the range of the sanner, the elapsed tme between emsson and reepton of the laser pulse served to alulate the dstane between objet and DLS [11]. Sne the refletvty was based on the materal and poston of the varous objets, the rangng error exsted n extrns albraton of amera-dls.ths work appled the least-squares method to lnearly ft the dsretely dstrbutng laser ponts, whh were loated on the surfae of a three-dmensonal retangular albraton objet, as the ntersetng lnes. Sne the laser rays from DLS were nvsble, the albraton data must be on the edges of albraton objets. However, DLS ould not Xw Yw Zw Ow detet the edge ponts of objet aurately beause of angular resoluton, whh also aused the nauray of DLS [1]. To solve ths problem, half of the value of angular resoluton was used as the nreased value of step-angular error to modfy the laser data ponts on the edges of objet. By mnmzng the re-projeton error between those adjusted ponts aptured by DLS and ther orrespondng projetons on the mage oordnate of the amera, the extrns albraton parameters were refned wth a general optmzaton. The rest of ths paper s as follows: Seton presents the prnple and notatons of extrns albraton. Seton 3 presents a new algorthm to mprove the auray of DLS for the aurate mprovement of extrns albraton between the amera and DLS. Compared wth related methods, the expermental results are desrbed n Seton 4. Lastly, Seton 5 onludes the algorthm n ths paper. II. THE CALIBRATION PROBLEM The amera an be desrbed by the perspetve pnhole model as shown n Fg.. A projeton of a random edge pont from the amera oordnates system P [ X, Y, Z ] T n the world oordnate to the mage oordnates p [ u, v] T an be represented as follows: u X Z f s u X 0 u 0 Y v. K. Y Z Z 0 fv v0 0 Z (1) where s a proportonal fator and K s the amera related to the amera s nternal struture. f u, f v are the equvalent foal lengths on u-axe and v-axe of the mage oordnate system respetvely. Here, (u 0,v 0 ) s alled the oordnates of the prnpal pont and s s the parameter desrbng the skewness of the two mage axes. Ths paper appled the Camera Calbraton Toolbox n referene [14] to alulate the amera ntrns matrx wth Matlab. A three-dmensonal albraton objet was vewed by a amera and DLS as shown n Fg.3. DLS ould detet dreton and dstane measurements of the objet lyng on a sannng plane parallel to the floor. The DLS oordnate system was defned wth an orgn at DLS, and the laser sannng plane was the plane Z l =ŋ, where ŋ s a onstant representng the dstane from the orgn of the DLS oordnate system to the orgn of the world oordnate system. Supposng an edge pont P w deteted by DLS was reported as P [ os( ), sn( ), ] T l D n D n n a normalzed Cartesan oordnate system, where δ s the angular resoluton, n s the number of laser beam, and D represents the dstane from the enter of DLS to the albraton objet. And P l was projeted n the amera oordnate system P as follows: P P l ()

3 JOURNAL OF MULTIMEDIA, VOL. 8, NO. 6, DECEMBER where s a 3 3 orthonormal matrx representng the rotaton matrx orrespondng to the 3 1 transformed vetor. Combnng (1) and () leads to the followng extend homogeneous equaton between the amera oordnate system and the DLS oordnate system: A. X b. (3) where A s a 3 1 matrx and b s a 3-vetor whh an T be expressed as b uz k, vz k, Z k, and X s a 9 1 vetor representng 1 unknown extrns albraton parameters. n pars of (P l, p) representng the projetons of the same pont P w vewed n the DLS and the amera were seleted to solve the overdetermned homogeneous equatons. When the value of n was greater than 4, the least square soluton of (3) was obtaned as followng: P L (4) The detals about ths matrx omputaton an be referred n Matrx Computaton [15]. Ths onluded the ntal rotate matrx and the transformed vetor n extrns albraton of amera-dls. (a) (b) Fgure 3. A three-dmensonal albraton objet n the both vews of a amera (a) and DLS (b) III. PROPOSED SCHEME Ths seton desrbed n detal the algorthm to mprove the auray of extrns albraton. A three-dmensonal retangular albraton objet was plaed at dfferent poses as long as ts feature ould be deteted by a amera and DLS. The method of least squares was used to lnearly ft laser data of the objet sanned by DLS for redung the rangng error. And half of the value of the angular resoluton was appled to modfy the edge laser ponts and the laser apexes of the objet. Lastly, the adjusted laser data ompared wth the nonlnear optmzaton and the general optmzaton was used to refne and of the extrns albraton between amera and DLS for aurate mprovement. A. Redung the Rangng Error The ombnaton of the rangng error and the step-angular error redued the auray of extrns albraton of amera-dls. Hene a new algorthm was proposed to redue rangng error to mprove the auray of laser data as shown n Fg.4 (a). A blak dot P ndated the atual measurement of the laser ponts and devated from the albraton objet surfae. And the green pont P represented the adjusted laser data orrespondng to P. Ths work appled the method of least squares to lnearly ft laser ponts of the albraton objet aptured by DLS as two ntersetng lnes (seeng the red lnes L and 1 L as shown n Fg. 4 (a)). The lnes represented the projeton of the albraton objet n the DLS oordnate system and were expressed as: w1 w1 w1 w1 L {( x, y ) y a x b, 1 k k k 1 k 1 k 1 k 1 k 1 k 1 x + y D } k k k m m m m \ L {( x, y ) y a x b, k k k k k w k w k w k w x + y D } k k k where (X k,y k ) represents the oordnate of the atual laser ponts and D k gves the dstane from the laser enter n DLS oordnate whh satsfes (5) D x + y, k k k k defnes the laser pont on the k-th beam, w stands for the number of laser beam at the mnmum dstane, a 1 and a are the slopes of the lnes, and b 1 and b represent the nterepts of lnes n DLS oordnate system. The nterepts and slopes were obtaned by usng the method of lnear fttng. The least squares resoluton was appled to express the lnear parameters of two ntersetng lnes L 1 and L as followng: w1 w1 w1 w1 w1 1 w 1 x y x y y a x k k k k k k k 1 k 1 k 1 k 1 k 1 1, b 1 w1 w1 w 1 w 1xk xk k1 k1 a a m m m m m m w 1 x y x y y a x k k k k k k k w k m k m k w k w, b w1 w1 m w 1 w 1xk xk k1 k1 Combnng (5) and (6), the optmzed laser ponts (green dots n Fg.4) orrespondng to the orgnal laser ponts (blak dots n Fg.4) were used to redue the rangng error for mprovng auray of laser data. B. Redung the Step-angular Error Takng nto onsderaton that the laser rays were nvsble, the albraton data must be on the edges of albraton objets. However, the edge ponts ould not be deteted aurately by DLS due to angular resoluton, whh was alled as the step-angular error. It was a man reason redung the auray of extrns albraton. When the laser rays ht an objet edge, the pont on the left edge of the albraton objet had a real world oordnate as B 1 = (X 1, Y 1, Z 1 ), whh polar oordnate ould be wrtten as B 1 = (,D). However, sne the DLS had an angular resoluton, a nearby deteted pont P 1 = (n,d) on the albraton objet was used to replae B 1. The step-angle error of the pont B 1 wth respet to the laser pont P 1 as (see Fg. 4 (b)), where s the nluded angle between B 1 and P 1. The orgnal data was refned as B 1 = (nd). Based on observatons and analyss, the value of satsfed two ondtons: Frstly, the step-angular error was always less than one. Beause f not, the pont B 1 must also be deteted by the laser and (6)

4 780 JOURNAL OF MULTIMEDIA, VOL. 8, NO. 6, DECEMBER 013 (n-1)δ P P' Three-dmentonal Calbraton Objet L1 (n+m-1)δ L nδ (n+1)δ wδ (n-1)δ (n+ξ)δ Three-dmentonal Calbraton Objet L1 B1 mδ B P1 ξδ nδ τδ wδ (w+1)δ B3 L (m-1)δ O D Laser Sanner O D Laser Sanner (a) (b) Fgure 4. Analyss of rangng error and step-angular error n extrns albraton t should represent the edge nstead of P 1.The seond ondton was that the laser ponts P met normal dstrbuton and ts mean approahes 1/, whh was hosen as the estmated value of step-angular error. Smlarly, the rght edge pont B and the apex pont B 3 of the albraton objet were also hose to alulate the parameters of extrns albraton (see Fg.4 (b)). Aordng to the lnear relatonshps of between L 1 and L, the followng equatons were obtaned: B X, Y X D os n, Y a X b ,,, os B X, Y X D os n, Y a X b A X Y Y a X b Y a X b B X Y X D Usng to estmate the nreasng value of step-angular error, the auray of laser data was mproved greatly as well as the auray extrns albraton n ths paper. C. Nonlnear Optmzaton Based on urrent adjusted laser data, a nonlnear optmzaton wth the Levenberg-Marquardt method was proposed [16] to redue the re-projeton error between the orgnal laser ponts and the optmzed laser ponts as followng: E arg mn w. B L, P P DLS w. B L, P P w. B L, P P ) where the left edge pont B 1, the rght edge pont B and the apex pont B 3 of the albraton objet were seleted to solve the nonlnear problem. where P 1 ndates the left edge pont of the albraton-objet projeted on the -th pose n DLS oordnate system, as same as the P orrespondng to the rght edge pont and P 3 orrespondng to apex pont. B 1, B and B 3 are the modfed ponts of orgnal laser ponts P1, P, P3 on the (7) (8) two ntersetng lnes. w1, w, w3 ndate the weght of the left edge pont, the rght edge pont and the apex pont at -th pose n whole progress of extrns albraton. EDLS denotes the re-projeton error of the orgnal laser ponts to the optmzed laser ponts. By mnmzng the Euldean dstane of the error E between the orgnal laser ponts and those DLS adjusted ones to refne laser data, the auray of laser data obtaned by DLS was mproved further. D. General Optmzaton The above soluton was obtaned by modfyng the laser data whh was not dretly related to extrns albraton of amera-dls. And both the amera and DLS had some noses n ther outputs whh affeted the fnal auray of extrns albraton. For the further aurate mprovement of extrns albraton, extrns parameters were nonlnearly refned wth a general optmzaton, whh was more physally meanngful. A parameter was defned to represent the Euldean dstane of the error from the modfed laser ponts to the orrespondng projetons n mage oordnate as followng:,,,, E f P x y z p u v L L L L (9) A nonlnear mnmzaton on E wth the Levenberg-Marquardt method was used to refne the rotate matrx and the transformed vetor of extrns albraton as followng: Eam DLS mn.. K.. PL p u, v (10) Z j where the ndex represents the pose number of the albraton objet, P L the j-th laser radar pont at the -th poses of the albraton objet n DLS oordnate, p u, v the projeton orrespondng to P represents n the mage oordnate system, and s the weght proporton of the -th pose n the overall data. Combnng (9) wth (10), a general nonlnear optmzaton was proposed by mnmzng the ombnaton of the error from the orgnal laser ponts to the optmzed laser ponts L

5 JOURNAL OF MULTIMEDIA, VOL. 8, NO. 6, DECEMBER and the error from the optmzed laser ponts to mage ponts as follows: E E E (11) general amdls DLS Here, s a salar weghtng parameter to normalze the relatve ontrbuton between Eam DLS and E DLS. Ths requres an ntal value of and n extrns albraton, whh s obtaned n the prevous seton. The general optmzaton of extrns albraton was arred to refne the extrns albraton parameters to mprove the auray of extrns albraton sgnfantly. A. Comparson IV. EXPERIMENTAL RESULTS The ntrns matrx of the amera was alulated wthn the Camera Calbraton Toolbox for Matlab proposed n [17] as: K And the proposed algorthm for the data modfyng and the aurate mprovement of extrns albraton has been mplemented n Matlab. Comparng the adjusted laser data wth the general optmzaton, the extrns albraton parameters and were refned wth the assumpton of 10 and Z. 950 as followng: [ , , 90] A three-dmensonal retangular albraton-objet was used for extrns albraton n ths paper. Eah plane of the albraton objet was defned by 10 6 grds and the sze of the pattern square was mm. The albraton objet was plaed at the dstane rangng from 1 meter to 5 meters away from the amera-dls system. In order to ompare wth the Zhang s algorthm (Zhang (004)) and the Sattaratnama s algorthm (Sattaratnama (011) ), Gaussan noses wth mean 0 and standard devaton 0.5 pxels were added to the projeted mage ponts of edge ponts and apexes of the albraton objet. A range of ±m as unform nose was also added nto the rangng measurement of laser ponts. 100 trals of ndependent poses were seleted to derease the nfluene of Gaussan noses. Several ontrast parameters were seleted to verfy hgh auray of albraton wth the new algorthm proposed n ths paper as showed n Table I. As showed n Table 1, the u-axs average error of ths algorthm was lmted nto 30 pxels, whh was nreased by 61.4% ompared wth Zhang (004) and by 5.8% ompared wth Sattaratnama (011). And the v-axs average error was lmted nto 3 pxels, whh was obvously mproved by 47.5% orrespondng to Zhang (004) and by 43.5% orrespondng to Sattaratnama (011). The u-axs and v-axs average errors were both presentng the extrns albraton aurate mprovement T of the new algorthm n the mage oordnate system. Here ths work appled mages of pxels to albraton proedure ompared wth ones of pxels n the paper proposed by Zhang (004) and ompared wth mages of pxels and pxels mentoned n Sattaratnama (011), whh presented hgher resoluton of amera n albraton. Ths aused a large magntude of the average errors n ths paper orrespondng to relatve works. The three-dmensonal error n ths algorthm, whh presented the albraton error n the rangng measurement, was about m, whh was less than the error about.49 m obtaned by the method n Zhang (004) and the error about 1.9 m orrespondng to Sattaratnama (011). Smlarly, the value of angle error n ths new algorthm obtaned the smallest value about degree n world oordnate system. The mnmal results of the three-dmensonal error and the angular error obtaned by the algorthm showed that, the albraton errors were weakly affeted by angles and poses of the albraton objet and the extrns albraton system of amera and DLS n ths algorthm was more stable and aurate. Whereas, the results obtaned by the method n Zhang (004) and Sattaratnama (011) were both strongly nfluened by ths angle and poses. TABLE I. EXPERIMENTAL RESULT OF NEW ALGORITHM COMPARED WITH RELATED WORKS Methods Zhang (004) Sattaratnama (011) New algorthm u-axs average error (pxel) v-axs average error (pxel) Three-dmensonal error (m) Angle error (degree) RMS (pxel) STD The Root Mean Square (RMS) of the albraton errors n ths algorthm was losed to 34.5 pxel, whh was the smallest among the three methods. The value of RMS n ths paper showed the obvous mprovement by 64.7% ompared wth Zhang (004) and by 8.3% orrespondng to Sattaratnama (011), whh ndated the hgher preson of the extrns albraton. What s more, the mnmum value of the Standard Devaton (STD) of the albraton errors presented that the error dstrbuton was not very dsrete and the extrns albraton was stable and robust n ths paper. A further experment dealng wth the nfluene of the number of data pars on the albraton error was performed. The number of the data pars was vared from 5 to 55 and the albraton error of every number was omputed by runnng 51 trals as showed n Fg.5. Where x-axs represents the number of the data pars and y-axs represents the albraton error. The new algorthm had the smallest albraton error urve whh showed more aurate n extrns albraton. What s more, the error urve of ths algorthm reahed a stable value at about 15

6 Three-dmensonal Error(m) Calbraton Error(pxel) 78 JOURNAL OF MULTIMEDIA, VOL. 8, NO. 6, DECEMBER 013 pars aganst to about 7 pars n Zhang (004) and Sattaratnama (011), whh showed the hgher speed n extrns albraton of ths algorthm Zhang(004) Sattaratnama(011) New Algorthm was omposed wth two planar albraton patterns, whh were defned by 10 6 grds. And eah square grd was 30 mm 30 mm. Ths albraton was desgned for ntrns albraton of amera and extrns albraton of amera-dls smultaneously for effeny mprovement and tme savng. Sne the mage sensor sze was.3 mm 14.9 mm and the amera foal length was fxed at 55mm, one pxel n mage oordnate system was equal to m n world oordnate system dependng on the resoluton of mage s 7dp. On real data, the method operates well gven relable albraton parameters of the amera Number of Data Pars Fgure 5. The nfluene of the number of data pars on the albraton error Zhang(004) Sattaratnama(011) New Algorthm Angles of Calbraton Objet (degree) Fgure 6. The nfluene of the angles of the albraton objet on the three-dmensonal error Ths experment was performed to reveal the nfluene of the angles of the albraton objet on the three-dmensonal error as showed n Fg.6. Where x-axs represents the rotaton degree of the albraton objet hanged from 0 to 90 degree every 3 degree. And the y-axs represents the three-dmensonal error. The result of Zhang (004) and Sattaratnama (011) However, the results n the new algorthm were weakly affeted by the angles from the albraton objet to the DLS sle plane. whle the results obtaned by the method n Zhang (004) and Sattaratnama (011) are strongly nfluened by ths angle. Therefore, t an be onluded that the desgn of the three-dmensonal retangular albraton objet s optmal n terms of mnmzaton of albraton errors. B. Expermental Results wth Real Data Experments were arred out on the equpment as shown n Fg. 1. A CANOY EOS550D SLR amera wth mages of pxels resoluton was mounted on a SICK LMS91-S05 laser sanner. Ths two-dmensonal laser sanner provdes range measurements by sannng 180 degrees of the envronment parallel to the floor and maxmum 80 (m) measurements wth 0.5 degree angular resoluton. A three-dmensonal retangular albraton-objet was moved n front of amera and DLS at the dstane rangng from 1 meter to 5 meters for extrns albraton n ths work. The albraton objet Fgure 7. Projeton of the DLS ponts of the albraton objet nto the mages. Red ponts represented the projeton usng the extrns albraton results obtaned wth the new algorthm orrespondng to blue ponts obtaned by Zhang (004) and green ponts obtaned by Sattaratnama (011). It was obvously showed that the new algorthm had the best performane n extrns albraton of amera-dls. Comparng wth Zhang (004) and Sattaratnama (011), the DLS ponts were projeted nto the mages usng the optmzed extrns albraton results obtaned n ths paper as shown n Fg.7. Obvously, t onluded that the new algorthm ould mprove the auray of extrns albraton greatly. V. CONCLUSIONS In ths paper, a new algorthm was proposed to mprove auray of laser data to be used n extrns albraton between amera and DLS.The least-squares method for redung the rangng error and an angular estmaton for redung the step-angular error were appled to modfy the laser data of the three-dmensonal retangular albraton objet obtaned by DLS. Fnally, by mnmzng re-projeton error between adjusted laser ponts and ther orrespondng projetons on the mage oordnate, extrns parameters were refned generally to mprove the auray of extrns albraton. Comparng wth Zhang (004) and Sattaratnama (011), ths algorthm has the advantages of beng fast to albrate and yeldng better performane. Expermental results showed that the angular error was down to about 0. degree and the three-dmensonal error was down to about 1 m n the measurng range from 1m to 5m. And the auray of extrns albraton of amera-dls has been verfed to mprove greatly. ACKNOWLEDGMENT Ths study s fnanally supported by Natonal Natural Sene Foundaton of Chna (Grant No ), Chna Postdotoral Sene Foundaton (Grant No. 01M510330), 948 projet supported by State Forestry Admnstraton, Chna (Grant No ).

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